MILAN—Italian bank UniCredit is set to sell a slice of one of its prized assets—online bank Fineco—in the latest example of banks' putting their houses in order ahead of a health check later this year.

A person with knowledge of the preparations said Italy's largest bank by assets may announce its plans for an initial public offering of between 25% and 30% of Fineco on Tuesday, when it publishes its fourth-quarter results and a strategic plan for the next few years. An IPO could value Italy's most successful online banking...